Nineteen cholesterol derivatives containing a variety of azobenzene moieties coupled to C-3 of a steroidal moiety through an ester linkage were synthesized. We employed two different esterification methods by which cholesterol derivatives with the natural (.^-configuration at C-3 and those with the inverted (/^-configuration at C-3 were obtained (the latter derivatives are indicated by a prime). Among them, cholesterol derivatives bearing a p-alkoxyazobenzene moiety (2R and 2R') acted as excellent thermally-reversible gelators of various organic fluids, but the gelation ability is fairly different between 2R and 2R': 2R could gelatinize hydrocarbons such as n-hexane, n-octane, and toluene, halogen solvents such as 1,2-dichloroethane and dichloromethane, ether solvents such as diethyl ether and THF, and alcohols such as ethanol and 1-butanol whereas 2R' could gelatinize ketones, methanol, and polysiloxanes. In general, the solubility of 2R' in apolar solvents is superior to that of 2R, so 2R is useful for gelation of apolar solvents whereas 2R' is useful for gelation of polar solvents. We found that the sol-gel phase transition is sensitively "read-out" by a change in the circular dichroism (CD) spectrum: the gel phase is CD-active whereas the sol phase is totally CD-silent. For example, the 2Me-l-butanol gel gave a positive exciton coupling band with (R)-chirality whereas the 2EFmethanol gel gave a negative exciton coupling band with (5)-chirality. These results mean that dipoles in the azobenzene moiety are oriented in a clockwise (in (R)-chirality) or anticlockwise (in (5")-chirality) direction when they interact in the excited state. Strangely, we accidentally found that the CD sign of the gels prepared from 2Pr, 2Bu, and 3Me? (azobenzene-linked cholesterol derivative with p-NMe2) is frequently inverted. After careful examination of the gel preparation conditions, we found that inversion takes place only when the cooling speed is fast. The scanning electron microscopic studies established that gelators form three-dimensional networks with helical fibrils. Interestingly, we found that in the 3Me' gel prepared from cyclohexane the gel with (R)-chirality in CD possesses a right-handed helix whereas the gel with (S)-chirality in the CD possesses a left-handed helix. The sol-gel phase transition was also induced by photoresponsive cis-trans isomerism of the azobenzene moiety: the gel formed from the franr-isomer was efficiently converted to the sol when trans-to-cis isomerization was photochemically induced, and this process can be repeated reversibly. The photoinduced sol-gel phase transition was also "read-out" as a change in CD spectroscopy.

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We define a toric degeneration of an integrable system on a projective manifold, and prove the existence of a toric degeneration of the Gelfand-Cetlin system on the flag manifold of type A. As an application, we calculate the potential function for a Lagrangian torus fiber of the Gelfand-Cetlin system.

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We study the spaces of locally finite stability conditions on the derived categories of coherent sheaves on the minimal resolutions of A n -singularities supported at the exceptional sets. Our main theorem is that they are connected and simply-connected. The proof is based on the study of spherical objects in [30] and the homological mirror symmetry for A n -singularities.

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Masahito YamazakiDepartment of Physics, University of Tokyo, Hongo 7-3-1, Tokyo, 113-0033, Japan E-mail: yamazaki@hep-th.phys.s.u-tokyo.ac.jp Abstract: We propose a new method to find gravity duals to a large class of threedimensional Chern-Simons-matter theories, using techniques from dimer models. The gravity dual is given by M-theory on AdS 4 × Y 7 , where Y 7 is an arbitrary seven-dimensional toric Sasaki-Einstein manifold. The cone of Y 7 is a toric Calabi-Yau 4-fold, which coincides with a branch of the vacuum moduli space of Chern-Simons-matter theories.